Question

System shown in the diagram is in equilibrium. Suddenly string between A and B is cut, then initial tension in upper spring is:

• A. $zero$
• B. $mg$
• C. $2mg$
• D. $3mg$

Answer 1

The correct option is D $3mg$

Let the tension in the upper string be $T$, tension in middle string be $T_1$ and tension in the lower string be $T_2$

Equation of motion of the upper block

$T=T_1+mg$

Equation of motion of the middle block block

$T_1=T_2+mg$

Equation of motion of the lower block

$T_2=mg$

As the string between $AB$ is cut, the only force remains is $T$ whic is equal to $3mg$.